Mathematics Commons^™

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

A Generalization Of The Graham-Pollak Tree Theorem To Even-Order Steiner Distance, Joshua Cooper, Gabrielle Tauscheck

Faculty Publications

Graham and Pollak showed in 1971 that the determinant of a tree’s distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. The Steiner distance of a collection of k vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices; for k = 2, this reduces to the ordinary definition of graphical distance. Here we show that the hyperdeterminant of the kth order Steiner distance hypermatrix is always nonzero if k is even, extending their result beyond k = 2. Previously, the authors showed that the k-Steiner …

Constacyclic Codes Of Length With Three Prime Factors And Primitive Idempotents, Supakarn Rakphon

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let Fq be a finite field of order q and t be a prime such that q t − 1 = l v1 1 l v2 2 l v3 3 c where l1, l2, l3 are distinct odd primes with gcd(l1l2l3, q(q−1)) = 1 and c is a positive integer with gcd(l1l2l3, c) = 1. In this thesis, we find all irreducible divisors of x l m1 1 l m2 2 l m3 3 −a over Fq and all generator polynomials for constructing a-constacyclic codes of length l m1 1 l m2 2 l m3 3 . In addition, we …

Contrastive Learning, With Application To Forensic Identification Of Source, Cole Ryan Patten

Electronic Theses and Dissertations

Forensic identification of source problems often fall under the category of verification problems, where recent advances in deep learning have been made by contrastive learning methods. Many forensic identification of source problems deal with a scarcity of data, an issue addressed by few-shot learning. In this work, we make specific what makes a neural network a contrastive network. We then consider the use of contrastive neural networks for few-shot learning classification problems and compare them to other statistical and deep learning methods. Our findings indicate similar performance between models trained by contrastive loss and models trained by cross-entropy loss. We …

Optimal Network Analysis Through Vertex Order Coloring Of Intuitionistic Fuzzy Graph Operations, A. Meenakshi, S. Dhanushiya, Hong Qin, Maniyandy Elangovan

Data Science Faculty Publications

Intuitionistic fuzzy graphs IFGs are a powerful tool for modeling uncertainty and complex relationships. They offer versatile frameworks for addressing real-world challenges. In this research, we have introduced intuitionistic fuzzy vertex order coloring IFVOC and analyzed the alpha-strong (alpha str), beta-strong (beta str), and gamma-strong (gamma str) vertices through their degree. We explored important theorems based on the types of strong vertices, broadening the scope of our study. We analyzed multiple IFG products to determine the most optimal network based on some important metrics, including the weight and total number of alpha str vertices, the chromatic number, and the weight …

Partial Collisions Of Unmater-Matter, Unmatter-Antimatter, And Unmatter1-Unmatter2 To Generate High Energy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present the possibility of partial collisions between unmatter with matter, and unmatter with antimatter, and two or more different types of unmatters colliding between themselves to create high energy. In general, the collisions between unmatter with matter, or with antimatter, or with other type of unmatter, because being partial, they release less energy than the matter-unmatter collision which is a total collision. But the unmatter may be easier to produce in laboratory than antimatter.

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Introduction To Upside-Down Logic: Its Deep Relation To Neutrosophic Logic And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that …

Remark On Falaco Soliton As A Tunneling Mechanism In A Navier-Stokes Universe, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is a follow up to our previous article [1] suggesting that it is possible to find tunneling time solutions for Schrodinger equation considering quasicrystalline as interstellar matter, by virtue of quasicrystalline potential. The paper also discusses the mapping of these equations to Riccati equations, a class of nonlinear differential equations. This mapping can provide insights into the behavior of the Navier-Stokes equations and may lead to new methods for solving them. The Navier-Stokes equations, a set of nonlinear partial differential equations, are fundamental in fluid mechanics. They describe the motion of viscous fluids. In three dimensions, these equations …

Resolving The Paradoxism With The Logic Of “Not” In Javanese Puppetry: A Re-Reading Of Wrekodoro And Dewaruci’S Mytology, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There are a large number of text collections in Indonesia, related to wayang theme, cf Zoetmulder (1971). And the text collections do not consist only of wayang purwa but also variations of this theme, including wayang wahyu etc. In the mean time, a Japanese scholar Shoshichi Nagatomo proposed the concept of "Asian Logic" which differs from Western logic. In Western thought, things are often seen as black or white, good or bad. However, Asian logic embraces certain degree of ambiguity. Here, "good" characters can exhibit flaws, and "bad" characters can possess redeeming qualities; especially among Javanese people preference is given …

Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.

Row-Column Designs: A Novel Approach For Analyzing Imprecise And Uncertain Observations, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Classical row-column designs cannot be applied when the underlying data set contains some imprecise, uncertain, or undetermined observations. In this paper, we discuss row-column design under a neutrosophic statistical framework. A significant contribution of our study is to propose a novel approach to analyzing row-column designs using neutrosophic data. This approach involves calculating the neutrosophic analysis of variance (NANOVA) table for the proposed design and using it to derive the FN -test in an uncertain environment. Two numerical examples have been used to assess the proposed design’s performance. Results from the study indicated that a row column design under …

Extremal Graphs For Widom–Rowlinson Colorings In K-Chromatic Graphs, John Engbers, Aysel Erey

Mathematical and Statistical Science Faculty Research and Publications

The Widom–Rowlinson graph, H_WR , is the fully looped path on three vertices. Let hom(G,H_WR) be the number of graph homomorphisms from G to H_WR or, equivalently, the number of H_WR-colorings of G. We investigate extremal graphs for hom(G,H_WR) for G in the family of k-chromatic graphs subject to various connectivity requirements. In particular, we determine the graphs G maximizing hom(G,H_WR) in the families of n-vertex k-chromatic graphs, n-vertex connected k-chromatic graphs, n-vertex k-chromatic graphs with c components, n …

Use Of Hydroxychloroquine In Multidrug Protocols For Sars-Cov-2, Eleftherios Gkioulekas, Peter A. Mccullough

School of Mathematical & Statistical Sciences Faculty Publications

We review the available evidence supporting the use of hydroxychloroquine-based multidrug protocols in the treatment of COVID-19, in response to a recently published editorial in the Tasman Medical Journal.

Multicolor Bipartite Ramsey Number Of Double Stars, Gregory M. Decamillis

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. The $k$-color bipartite Ramsey number of $ S(n,m)$, denoted by $r_{bip}(S(n,m);k)$, is the smallest integer $N$ such that, in any $k$-coloring of the edges of the complete bipartite graph $K_{N,N}$, there is a monochromatic copy …

Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola

Mathematics Faculty Publications

No abstract provided.

Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Operations Research (OR) is a required course in any applied math program in the Philippines. It involves complex and computation-heavy algorithms to guide and improve decision-making in organizations and relevant contexts. Despite the advent of software that have automated the computations or the implementation of algorithms, the teaching and learning of OR may still be rife with procedures being performed manually by hand. In this paper, we report on our initial progress on a research project that aims to revise the OR syllabi in one Philippine university, by integrating more technological tools in the teaching and learning of OR for …

Adjusting For Participation Bias In Case-Control Genetic Association Studies For Rare Diseases, Le Wang, Ben Fitzpatrick, Zhengbang Li, Clarice Weinberg, Jinbo Chen

Mathematics, Statistics and Data Science Faculty Works

Collection of genotype data in case-control genetic association studies may often be incomplete for reasons related to genes themselves. This non-ignorable missingness structure, if not appropriately accounted for, can result in participation bias in association analyses. To deal with this issue, Chen et al. [7] proposed to collect additional genetic information from family members of individuals whose genotype data were not available, and developed a maximum likelihood method for bias correction. In this study, we develop an estimating equation approach to analyzing data collected from this design that allows adjustment of covariates. It jointly estimates odds ratio parameters for genetic …

Rising Plant Demand Strengthens Nitrogen Limitation In Tidal Marsh, Le Wang, Adam Langley, Bella Yedman, Patrick Megonigal

Mathematics, Statistics and Data Science Faculty Works

Nitrogen (N) is a limiting nutrient for primary productivity in most terrestrial ecosystems, but whether N limitation is strengthening or weakening remains controversial because both N sources and sinks are increasing in magnitude globally. Temperate marshes are exposed to greater amounts of external N inputs than most terrestrial ecosystems and more than in preindustrial times owing to their position downstream of major sources of human-derived N runoff along river mouths and estuaries. Simultaneously, ecosystem N demand may also be increasing owing to other global changes such as rising atmospheric [CO2]. Here, we used interannual variability in external drivers and variables …

Persistent Relative Homology For Topological Data Analysis, Christian J. Lentz

Mathematics, Statistics, and Computer Science Honors Projects

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via the language of persistent homology, which encodes features of interest as holes within a filtration of the data. The recently presented U-Match Decomposition places the standard persistence computation in a flexible form, allowing for straight-forward extensions of the algorithm to variations of persistent homology. We describe U-Match Decomposition in the context of persistent homology, and extend it to an algorithm for persistent relative homology, providing proofs for the correctness and stability of the presented algorithm.

An Investigation Of Students' Modes Of Thinking Concerning Linearity In Linear Algebra, Noa Levy

Honors Undergraduate Theses

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary …

GröBner Bases With An Application To Tame Functions, Jessica D. Marconi

UNF Graduate Theses and Dissertations

Grobner bases are essential tools in algebraic geometry, used to simplify and solve systems of polynomial equations. These bases revolutionized computational methods in various branches of mathematics after being introduced in 1965 by Bruno Buchberger. This thesis explores the foundational concepts of Grobner bases, including their formation and properties. It also demonstrates their use in solving mathematical problems in algebraic geometry, including the ideal membership problem. As an application, we show how Grobner bases can be used to determine whether a polynomial mapping is tame. This concept is crucial for analyzing the topology near singular points and establishing whether a …

Enumeration Of Lattice Paths With Restrictions, Vince White

College of Graduate Studies: Theses & Dissertations

Lattice path enumeration, through the lens of Catalan numbers, plays a crucial role in combinatorics. This thesis delves into enumerations of some of the most common lattice paths – north-east paths, up-down paths, and Dyck paths – with restrictions applied. The first restriction is counting north-east lattice paths that only cross the diagonal line, y=x, once. The second form of lattice paths with restrictions is up-down paths that cross the x-axis exactly once and fall to a fixed depth of k. While working through this module, a novel proof for a known integer sequence was used, then applied to generate …

Graph Coloring Reconfiguration, Reem Mahmoud

Theses and Dissertations

Reconfiguration is the concept of moving between different solutions to a problem by transforming one solution into another using some prescribed transformation rule (move). Given two solutions s₁ and s₂ of a problem, reconfiguration asks whether there exists a sequence of moves which transforms s₁ into s₂. Reconfiguration is an area of research with many contributions towards various fields such as mathematics and computer science.
The k-coloring reconfiguration problem asks whether there exists a sequence of moves which transforms one k-coloring of a graph G into another. A move in this case is a type …

Problems In Graph Theory With Applications To Topology And Modeling Rna, Rayan K. Ibrahim

Theses and Dissertations

In this thesis, we explore four projects. In the first project, we explore $r$-neighbor bootstrap percolation on a graph $G$. We establish upper bounds for the number of vertices required to percolate in the case that $r=2$ for particular classes of graphs. In the second project, we study the structure of graphs with independence number two. We prove a lower bound on the number of edges of such graphs, related to an upper bound on the number of edges in a triangle-saturated graph, and give a sufficient forbidden induced subgraph condition for independence number two graphs. In the third project, …

Torricelli's Law And The Turn-Up Number, Bianca K. Hampel

Theses and Dissertations

We investigate Torricelli's differential law for solids of revolution. Computing the ratio of times of drainage under the same circumstances (same existing requirements) but rotating the solids 180 degrees allows us to define a "Torricelli turn-up number" associated with the solid. For various solids, we calculate this turn-up number and construct solids that are not symmetric under the 180-degree rotation but with a turn-up number of 1. That allows us to construct nonsymmetric clepsydra.

A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig

Electronic Theses & Dissertations (2024 - present)

An analogue to Wolff's ideal problem for the multiplier algebra of the Dirichlet space, the main theorem provides sufficient conditions to classify membership of an arbitrary function in an infinitely generated ideal of the multiplier algebra.

Random Forests Regression For Soft Interval Data, Paul Gaona-Partida, Chih-Ching Yeh, Yan Sun, Adele Cutler

Mathematics and Statistics Faculty Publications

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L₂ type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as …

On The Structure Of Repeated-Root Polycyclic Codes Over Local Rings, Maryam Bajalan, Edgar Martinez-Moro, Reza Sobhani, Steve Szabo, Guelsuem Goezde Yilmazguc

EKU Faculty and Staff Scholarship

This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the perpendicular to 0-dual code for a given polycyclic code. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Paley Graphs, Prime Graphs, And Crossword Puzzles, Robert D. Jacobs Jr.

Theses and Dissertations

In this paper, we will talk about many different mathematical concepts. We will prove theorems about Paley graphs, prime graphs, and crossword puzzles. It will be very fun.

The results in the section about Paley graphs include structure theorems about the subgraph induced by the quadratic residues, the subgraph induced by the non-residues and a few related subgraphs. The main is to better understand the “independence structure” of the Paley graph itself. No good upper bound on the independence number of Paley graphs is known. Theorems about these subgraphs, and various counts aim at future improvement of upper bounds for …